Title:         A Finite Element Method for the Approximation of
               the Incompressible, Linearized Euler Equations

Authors:       Richard S. Falk and Gerard R. Richter

Source:        Advances in Computer Method for Partial Differential Equations
               VII, R. Vichevetsky, D. Knight and G. Richter (Eds.),
               1992, IMACS

Status:        Published

Abstract:      We present a finite element method for the transient,
               linearized, incompressible Euler equations in two space
               dimensions.  The velocity equations are discretized via the
               discontinuous Galerkin method over a space-time mesh of
               tetrahedrons.  The mesh is assumed to have been constructed in
               such a way that the tetrahedrons can be ordered explicitly with
               respect to velocity evolution.  For $n\ge 0$, the method yields
               a discontinuous piecewise polynomial approximation of degree
               $n$ for velocity and a continuous approximation of degree $n+1$
               for pressure.  We derive error estimates of order $h^{n+1/2}$
               for velocity and $h^{n-1/2}$ for the pressure gradient.


Keywords:      

Subj. Class.   

URL:           http://www.math.rutgers.edu/~falk/papers/euler.pdf